All told, this is a totally minor complication of the Israeli-Palestinian conflict.
I noticed last night before I went to bed that my cell phone was showing a time one hour earlier than my watch and my laptop clock, despite having been correct earlier. I figured that it somehow was lagging due to my travel from Britain earlier in the day, so I turned it off, turned it back on, found it to be showing the right time, set the alarm, and went to sleep.
I woke up early, saw that it was five minutes to six, and went back to sleep, intending to get back up when my alarm would go off at seven. Next thing I know, it's 8:20. My first thought was that I must have inadvertently set my alarm for 7pm, but I found it set for 7am, and still on — so it's not that I heard the alarm and turned it off in such a deep sleep that I didn't remember having done it. And then suddenly my phone switched to showing 7:20 as the current time. My watch had 8:20.
It turned out that, apparently, all night my phone had been cycling between picking up a signal from Hebron and one in Jerusalem, and it kept resetting its own clock accordingly, as Israel and the West Bank do not share a time zone.
Unfortunately, this means I won't be able to get a space at the library today, as you have to be there promptly at 9am; but I've got the phone force-set to the right time zone, so this shouldn't be a problem going forward.
Updated, 3:52 pm, Jerusalem time. The weather app also has me in the wrong place (I'm in West Jerusalem), but this strikes me as oddly specific: